1. Field of the Invention
The present invention relates to pole zero correction generally and, more particularly, to a novel instant pole-zero corrector for digital radiation spectrometers and the same with automatic attenuator calibration.
2. Background Art
The problem of pole-zero cancellation was recognized at the early development of charge sensitive preamplifiers for radiation spectroscopy. See, for example, C. H. Nowlin and J. L. Blankenship, xe2x80x9cElimination of Undesirable Undershoot in the Operation and Testing of Nuclear Pulse Amplifiersxe2x80x9d, Rev. Sci. Instr., Vol 36, 12, pp 1830-1839, 1965. The charge sensitive preamplifier produces a voltage step that is proportional to the collected charge from the radiation detector. The charge-to-voltage conversion is achieved by using a capacitor as a negative feedback element of a low noise amplifier. The capacitor accumulates the input charge, which leads to constant increase of the output voltage of the amplifier. Supply voltages limit the output dynamic range of the preamplifier. Therefore, the total charge accumulated across the feedback capacitor is also limited.
To maintain a linear operation of the preamplifier, it is necessary to discharge (reset) periodically the feedback capacitor or to bleed the capacitor charge continuously through a resistor connected in parallel with the feedback capacitor. The first type of preamplifier is known as a xe2x80x9cresetxe2x80x9d feedback charge sensitive preamplifier. The pole-zero cancellation is associated with the second type of preamplifier often referred to as a xe2x80x9cresistivexe2x80x9d feedback preamplifier. Hereafter in this description, this type of preamplifier will be simply called a xe2x80x9cpreamplifierxe2x80x9d. A simplified diagram of the preamplifier is shown in FIG. 1.
When radiation interact with the detector a short current pulse I(t) is produced. The response of the preamplifier to this current is Vp(t). A simple analysis of the circuit can be carried out in the frequency domain xe2x88x92I(s), Vp(s). The input impedance of the preamplifier is             Z      i        =          1                        C          i                ⁡                  (                      s            +                          1                              τ                i                                              )                      ,
The feedback impedance is             Z      f        =          1                        C          f                ⁡                  (                      s            +                          1                              τ                f                                              )                      ,
where xcfx84f=CfRf. For simplicity it is assumed that the gain A of the amplifier is frequency-independent.
The transfer function of the preamplifier can be found by solving the following system of equations:
I(s)=Ii(s)+If(s)xe2x80x83xe2x80x83(1)
                                                        I              1                        ⁡                          (              s              )                                ·                                    Z              1                        ⁡                          (              s              )                                      =                  -                                                    V                p                            ⁡                              (                s                )                                      A                                              (        2        )            xe2x80x83Ii(s)xc2x7Zi(s)xe2x88x92Vp(s)=If(s)xc2x7Zf(s)xe2x80x83xe2x80x83(3)
where, Il(s) and If(s) are the currents flowing through the input impedance and the feedback impedance respectively.
After solving the system of equations (1) to (3) the transfer function is found to be:                                           H            p                    ⁡                      (            s            )                          =                                                            V                p                            ⁡                              (                s                )                                                    I              ⁡                              (                s                )                                              =                      1                                          1                                  A                  ·                                                            Z                      i                                        ⁡                                          (                      s                      )                                                                                  +                                                A                  +                  1                                                  A                  ·                                                            Z                      f                                        ⁡                                          (                      s                      )                                                                                                                              (        4        )            
After substituting the expressions for ZI(s) and ZI(s) into (4), Hp(s) can be expressed as:                                           H            p                    ⁡                      (            s            )                          =                              A                          A              +              1                                                          (                                                C                  f                                +                                                      C                    i                                                        A                    +                    1                                                              )                        ⁢                          (                              s                +                                  1                                                                                                              R                          i                                                ⁢                                                  R                          f                                                                                                                      R                          i                                                +                                                                              R                            f                                                                                A                            +                            1                                                                                                                ⁢                                          (                                                                        C                          f                                                +                                                                              C                            i                                                                                A                            +                            1                                                                                              )                                                                                  )                                                          (        5        )            
Let                               C          p                =                  (                                    C              f                        +                                          C                i                                            A                +                1                                              )                                    (        6        )                                          R          p                =                                            R              i                        ⁢                          R              f                                                          R              i                        +                                          R                f                                            A                +                1                                                                        (        7        )                                          τ          p                =                              R            p                    ⁢                      C            p                                              (        8        )                                          k          p                =                              (                          A                              A                +                1                                      )                    ⁢                      1                          C              p                                                          (        9        )            
Using the new variables the preamplifier transfer function can be rewritten as:                                           H            p                    ⁡                      (            s            )                          =                              k            p                                s            +                          1                              τ                p                                                                        (        10        )            
Equation (10) represents a single real pole transfer function similar to the transfer function of a low-pass filter. For large gain of the amplifier (A greater than  greater than )             τ      p        ≈          τ      f        =                    R        f            ⁢              C        f            ⁢              xe2x80x83            ⁢      and      ⁢              xe2x80x83            ⁢              k        p              ≈                  1                  C          f                    ·      
From equation (10) the impulse response of the preamplifier can be found. The inverse Laplace transform gives the well known exponential response:                                           h            p                    ⁡                      (            t            )                          =                              k            p                    ⁢                      ⅇ                          -                              t                                  τ                  p                                                                                        (        11        )            
The response of the preamplifier to a detector current I(t) is given by the convolution integral:                                           v            p                    ⁡                      (            t            )                          =                                            ∫                              u                .                            t                        ⁢                                          I                ⁡                                  (                  λ                  )                                            ⁢                                                h                  p                                ⁡                                  (                                      t                    -                    λ                                    )                                            ⁢                              xe2x80x83                            ⁢                              ⅆ                λ                                              =                                    ∫              u              t                        ⁢                                          I                ⁡                                  (                  λ                  )                                            ⁢                              k                p                            ⁢                              ⅇ                                  -                                                            t                      -                      λ                                                              τ                      p                                                                                  ⁢                              xe2x80x83                            ⁢                              ⅆ                λ                                                                        (        12        )            
One important property of this response is that if the current has a finite duration, than the signal at the output of the preamplifier will decay exponentially after the current becomes zero. The decay time constant of the tail of the signal is the same as the decay time constant of the impulse response. FIG. 2 illustrates such response. The preamplifier response to a finite current signal can be easily derived from Equation (12). First, the detector current is defined as:                               I          ⁡                      (            t            )                          =                  {                                                                      I                  ⁡                                      (                    t                    )                                                                                                0                  ≤                  t                   less than                                       T                    c                                                                                                      0                                                                                  t                     less than                     0                                    ,                                      t                    ≥                                          T                      c                                                                                                                              (        13        )            
From Equations (12) and (13) the response of the preamplifier for t greater than Tc can be written as:                                           v            p                    ⁡                      (            t            )                          =                                            ∫              0                              T                c                                      ⁢                                          I                ⁡                                  (                  λ                  )                                            ⁢                              k                p                            ⁢                              ⅇ                                  -                                                            t                      -                      λ                                                              τ                      p                                                                                  ⁢                              xe2x80x83                            ⁢                              ⅆ                λ                                              =                                    k              p                        ⁢                          ⅇ                              -                                  t                                      τ                    p                                                                        ⁢                                          ∫                0                                  T                  c                                            ⁢                                                I                  ⁡                                      (                    λ                    )                                                  ⁢                                  k                  p                                ⁢                                  ⅇ                                      λ                                          τ                      p                                                                      ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  λ                                                                                        (        14        )            
where, the integral       ∫    0          T      c        ⁢      I    ⁢          (      λ      )        ⁢          k      p        ⁢          ⅇ              λ                  τ          p                      ⁢          xe2x80x83        ⁢          ⅆ      λ      
is a constant. Therefore, for t greater than Tc the preamplifier signal exponentially decays with the same time constant as given by the impulse response. FIG. 2 shows the preamplifier response to a finite detector current.
Due to various constraints such as noise performance and stability requirements, the preamplifier time constant is usually large. In order to optimize signal to noise ratio and to meet certain throughput requirements it is necessary to xe2x80x9cshortenxe2x80x9d the preamplifier exponential pulse. Traditionally, this is done using a CR differentiation network (CR high-pass filter). FIG. 3 shows a preamplifier-CR differentiator configuration.
The CR differentiation network plays an important role in analog pulse shapers. Digital pulse processors also benefit from digitizing short exponential pulsesxe2x80x94better utilization of ADC resolution, reduced pile-up losses, and simple gain control. The pole-zero cancellation is an important procedure for both analog and digital pulse processing systems.
When exponential pulses pass through a CR differentiation, circuit the output signal is bipolar. The combined transfer function of the preamplifier-differentiator configuration can be written as:                               H          ⁡                      (            s            )                          =                                                            k                p                                            s                +                                  1                                      τ                    p                                                                        ⁢                          s                              s                +                                  1                                      τ                    d                                                                                =                                                    k                p                            ·              s                        ⁢                          1                              s                +                                  1                                      τ                    p                                                                        ⁢                          1                              s                +                                  1                                      τ                    d                                                                                                          (        15        )            
where xcfx84d=CdRd. The impulse response can be obtained from the inverse Laplace transformation:                               h          ⁡                      (            t            )                          =                              k            p                    ⁢                      1                                          1                                  τ                  d                                            -                              1                                  τ                  p                                                              ⁢                      (                                                            1                                      τ                    d                                                  ⁢                                  ⅇ                                      -                                          t                                              τ                        d                                                                                                        -                                                1                                      τ                    p                                                  ⁢                                  ⅇ                                      -                                          t                                              τ                        p                                                                                                                  )                                              (        16        )            
If the ratio between the time constants of the preamplifier and the differentiator is       w    =                  τ        p                    τ        d              ,
then Equation (16) can be rewritten as:                               h          ⁡                      (            t            )                          =                                            k              p                        ⁢                          w                              w                -                1                                      ⁢                          (                                                ⅇ                                      -                                          t                                              τ                        d                                                                                            -                                                      1                    w                                    ⁢                                      ⅇ                                          -                                              t                                                  τ                          p                                                                                                                                )                                =                                                    k                p                            ⁢                              w                                  w                  -                  1                                            ⁢                              ⅇ                                  -                                      t                                          τ                      d                                                                                            -                                          1                                  w                  -                  1                                            ⁢                              (                                                      k                    p                                    ⁢                                      ⅇ                                          -                                              t                                                  τ                          p                                                                                                                    )                                                                        (        17        )            
Equation 17 indicates that the response of the preamplifier-differentiator can be expressed as difference of two responses. Both responses represent single real pole systems. The second term in equation (17) is the response of the preamplifier attenuated by a factor of       1          w      -      1        ·
Thus, a single pole response with time constant xcfx84d can be achieved by simply adding a fraction   1      w    -    1  
of the preamplifier signal to the output of the differentiation network.
FIG. 4 shows a basic pole-zero cancellation circuit. The preamplifier signal is applied to a high-pass filter network and a resistive attenuator (e.g. trimpot). The high-pass filter output and the attenuated preamplifier signal are added together and than passed to the pulse shaper. In early designs the analog adder was built using passive componentsxe2x80x94resistors. Although simple, the resistive adder has a major drawbackxe2x80x94its impedance will change with the change of the trim-pot. As a result the pole-zero adjustment inevitably affects the high-pass filter time constant. This drawback can be overcome by using active components to sum the signals from the high-pass filter and the attenuator.
In early development of the spectroscopy pulse shapers, the pole-zero adjustment was performed manually. The manual adjustment is done using an oscilloscope as an inspection tool for under or overshoot of the differentiated and shaped pulse. The operator uses his/her visual judgment to properly adjust the pole-zero. The manual adjustment can be time consuming and often requires special skills to perform the task.
An automatic approach for pole-zero correction is described in U.S. Pat. Nos. 4,866,400 and 5,872,363, both titled AUTOMATIC POLE-ZERO ADJUSTMENT CIRCUIT FOR AN IONIZING RADIATION SPECTROSCOPY SYSTEM. The automatic setup combines a circuit similar to one described in Cover et al., xe2x80x9cAutomated Regulation of Critical Parameters and Related Design Aspects of Spectroscopy Amplifiers with Time-Invariant Filtersxe2x80x9d, IEEE Trans. Nucl. Sci., Vol 29, No. 1, pp 609-613, February 1982. This circuit estimates whether the signal (after differentiation and pulse shaping) has an undershoot or an overshoot. In addition to the undershoot/overshoot estimator, the automatic pole-zero circuit comprises a control logic, a digitally controlled attenuator (MDAC), and current summer using an operational amplifier. This automatic pole-zero adjustment uses consecutive iterations. This is, it works on the principle of error-trial. In order to adjust the pole-zero, a large number of measurements are needed. The iterative algorithm can be time consuming, requiring a large number of measurements. In addition, the termination of the iterative process may result in miss-adjustments. Due to the requirement for a large number of pulse measurements, this iterative pole-zero adjustment scheme can be a major limitation when the detector counting rates are very low. The algorithms of the above patents are based on trail-error sequence and do not assume any knowledge or measurement of the parameters of the system.
Accordingly, it is a principal object of the present invention to provide a pole-zero corrector for digital radiation spectrometers that is essentially instant.
A further object of the present invention is to provide pole-zero corrector for digital radiation spectrometers that includes automatic attenuator calibration.
Another object of the invention is to provide such correctors that are easily implemented.
Other objects of the invention, as well as particular features, elements, and advantages thereof, will be elucidated in, or be apparent from, the following description and the accompanying drawing figures.
The present invention achieves the above objects, among others, by providing, in one preferred embodiment, method and means for instant pole-zero correction for digital radiation spectrometers. In another embodiment, there is provided method and means for instant pole-zero correction for digital radiation spectrometers with automatic attenuator calibration.